In recent years, optical fields manipulation has become a hot research topic and optical coherence manipulation can induce many novel physical effects. The laser beams with special correlation structure obtained by coherence control not only exhibit peculiar propagation characteristics, but also can effectively reduce the negative effects induced by atmospheric turbulence, such as intensity degradation, beam wander, scintillation and depolarization. Thus, these beams have applications prospects in free-space optical communications. In this paper, the basic theory of the construction of special correlation structure beams and the research methods as well as their development history are reviewed, and the propagation properties of special correlation structure beams in turbulent atmosphere in recent years are illustrated as examples.